相关论文: Assortative Exchange Processes

We investigate a system of interacting clusters evolving through mass exchange and supplemented by input of small clusters. Three possibilities depending on the rate of exchange generically occur when input is homogeneous: continuous…

The exchange-driven growth model describes the mean field kinetics of a population of composite particles (clusters) subject to pairwise exchange interactions. Exchange in this context means that upon interaction of two clusters, one loses…

We consider a system of clusters made of elementary building blocks, monomers, and evolving via collisions between diffusing monomers and immobile composite clusters. In our model, the cluster-monomer collision can lead to the attachment of…

We study a discrete model for generalized exchange-driven growth in which the particle exchanged between two clusters is not limited to be of size one. This set of models include as special cases the usual exchange-driven growth system and…

We introduce a mean-field framework for the study of systems of interacting particles sharing a conserved quantity. The work generalises and unites the existing fields of asset-exchange models, often applied to socio-economic systems, and…

Admissible chains of i-boxes are important combinatorial tools in the monoidal categorification of cluster algebras, as they provide seeds of the cluster algebra. In this paper, we explore the properties of maximal commuting families of…

In a geographically distributed population, assortative clustering plays an important role in evolution by modifying local environments. To examine its effects in a linear habitat, we consider a one-dimensional grid of cells, where each…

The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between…

Field-theoretic models have been used extensively to study the phase behavior of inhomogeneous polymer melts and solutions, both in self-consistent mean-field calculations and in numerical simulations of the full theory capturing…

Assortative mixing in networks is the tendency for nodes with the same attributes, or metadata, to link to each other. It is a property often found in social networks manifesting as a higher tendency of links occurring between people with…

The exchange graph of a cluster algebra encodes the combinatorics of mutations of clusters. Through the recent "categorifications" of cluster algebras using representation theory one obtains a whole variety of exchange graphs associated…

The behaviour and functioning of a variety of complex physical and biological systems depend on the spatial organisation of their constituent units, and on the presence and formation of clusters of functionally similar or related…

Distributed securities exchanges may become de facto fragmented if they span geographical regions with asymmetric computer infrastructure. First, we build an economic model of a decentralized exchange with two miner clusters, standing in…

We study theoretically in the present work the self-assembly of molecules in an open system, which is fed by monomers and depleted in partial or complete clusters. Such a scenario is likely to occur for example in the context of viral…

We investigate analytically and numerically a system of clusters evolving via collisions with clusters of minimal mass (monomers). Each collision either leads to the addition of the monomer to the cluster or the chipping of a monomer from…

This paper considers networks where relationships between nodes are represented by directed dissimilarities. The goal is to study methods that, based on the dissimilarity structure, output hierarchical clusters, i.e., a family of nested…

The inclusion of a fragmentation mechanism in population balance equations introduces complex interactions that make the analytical or even computational treatment much more difficult than for the pure aggregation case. This is specially…

We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under…

Species sampling processes have long served as the fundamental framework for modeling random discrete distributions and exchangeable sequences. However, data arising from distinct but related sources require a broader notion of…

A general relation for the dependence of nearest neighbor degree correlations on degree is derived. Dependence of local clustering on degree is shown to be the sole determining factor of assortative versus disassortative mixing in networks.…